Measuring frequency domain granger causality for multiple blocks of interacting time series
In the past years, several frequency-domain causality measures based on vector autoregressive time series modeling have been suggested to assess directional connectivity in neural systems. The most followed approaches are based on representing the considered set of multiple time series as a realization of two or three vector-valued processes, yielding the so-called Geweke linear feedback measures, or as a realization of multiple scalar-valued processes, yielding popular measures like the directed coherence (DC) and the partial DC (PDC). In the present study, these two approaches are unified and generalized by proposing novel frequency-domain causality measures which extend the existing meas…
Information Decomposition in Bivariate Systems: Theory and Application to Cardiorespiratory Dynamics
In the framework of information dynamics, the temporal evolution of coupled systems can be studied by decomposing the predictive information about an assigned target system into amounts quantifying the information stored inside the system and the information transferred to it. While information storage and transfer are computed through the known self-entropy (SE) and transfer entropy (TE), an alternative decomposition evidences the so-called cross entropy (CE) and conditional SE (cSE), quantifying the cross information and internal information of the target system, respectively. This study presents a thorough evaluation of SE, TE, CE and cSE as quantities related to the causal statistical s…
Causal and Non-Causal Frequency Domain Assessment of Spontaneous Baroreflex Sensitivity after Myocardial Infarction
Acute myocardial infarction (AMI) is thought to alter the baroreflex control of arterial pressure. We tested this hypothesis investigating the changes of the cardiovascular response after AMI in comparison with young and old healthy controls studied at rest and during head-up tilt, using causal and non-causal frequency domain measures of the baroreflex sensitivity. Our results indicate: (i) the importance of using a causal approach that takes into account not only feedback but also feedforward effects in the study of interactions between the heart period and the arterial pressure; (ii) the compromised capacity of baroreceptors to control SAP fluctuations in post-AMI patients, both at rest a…
Determination of Synchronization of Electrical Activity in the Heart by Shannon Entropy Measure
In this paper we propose a new index of synchronization for the study of heart’s electrical activity during atrial fibrillation (AF). The index relies on the measure of the time delays between correspondent activations in two atrial electrograms and on the characterization of their dispersion by a measure of Shannon Entropy. The algorithm was validated on simulated signals mimicking different degree of synchronization. Results showed the index was able to discriminate among different levels of organization, provided that it works on series of at least 50 activations (time resolution of almost 10 sec during AF). Moreover, we applied the algorithm to real bipolar electrograms, obtained from a…
Assessment of mental stress through the analysis of physiological signals acquired from wearable devices
Mental stress is a physiological state that directly correlates to the quality of life of individuals. Generally speaking, but especially true for disabled or elderly subjects, the assessment of such condition represents a very strong indicator correlated to the difficulties, and, in some case, to the frustration that derives from the execution of a task that results troublesome to be accomplished. This article describes a novel procedure for the assessment of the mental stress level through the use of low invasive wireless wearable devices. The information contained in electrocardiogram, respiratory signal, blood volume pulse, and electroencephalogram was extracted to set up an estimator f…
Estimation of Granger causality through Artificial Neural Networks: applications to physiological systems and chaotic electronic oscillators
One of the most challenging problems in the study of complex dynamical systems is to find the statistical interdependencies among the system components. Granger causality (GC) represents one of the most employed approaches, based on modeling the system dynamics with a linear vector autoregressive (VAR) model and on evaluating the information flow between two processes in terms of prediction error variances. In its most advanced setting, GC analysis is performed through a state-space (SS) representation of the VAR model that allows to compute both conditional and unconditional forms of GC by solving only one regression problem. While this problem is typically solved through Ordinary Least Sq…
Entropy-Based Detection of Complexity and Nonlinearity in Short-Term Heart Period Variability under different Physiopathological States
We compare different estimators of a popular en-tropy-based nonlinear dynamic measure, i.e. the conditional entropy (CE), as regards their ability to assess the complexity and nonlinearity of short-term heart rate variability (HRV). The CE is computed using binning, kernel and nearest neighbor entropy estimators in HRV time series measured from young, old and post-myocardial infarction patients studied at rest and during orthostatic stress. We find that the three estimators yield similar patterns of CE, but different patterns of nonlinear dynamics, across groups and conditions. These results suggest that the strategy for CE estimation is not crucial for the quantification of complexity, but…
Information domain approach to the investigation of cardio-vascular, cardio-pulmonary, and vasculo-pulmonary causal couplings
The physiological mechanisms related to cardio-vascular (CV), cardio-pulmonary (CP), and vasculo-pulmonary (VP) regulation may be probed through multivariate time series analysis tools. This study applied an information domain approach for the evaluation of non-linear causality to the beat-to-beat variability series of heart period (t), systolic arterial pressure (s), and respiration (r) measured during tilt testing and paced breathing (PB) protocols. The approach quantifies the causal coupling from the series i to the series j (C(ij)) as the amount of information flowing from i to j. A measure of directionality is also obtained as the difference between two reciprocal causal couplings (D(i…
Wave similarity mapping shows the spatiotemporal distribution of fibrillatory wave complexity in the human right atrium during paroxysmal and chronic atrial fibrillation.
Introduction: The complexity of waveforms during atrial fibrillation may reflect critical activation patterns for the arrhythmia perpetuation. In this study, we introduce a novel concept of map, based on the analysis of the wave morphology, which gives a direct evidence in the human right atrium on the spatiotemporal distribution of fibrillatory wave complexity in paroxysmal (PAF) and chronic (CAF) atrial fibrillation. Methods and Results: Electrograms were recorded from a 64-electrode catheter in the right atrium of 15 patients during PAF (n = 8) and CAF (n = 7). Wave similarity maps were constructed by calculating the degree of morphological similarity of activation waves (S) at each atri…
A method for quantifying atrial fibrillation organization based on wave-morphology similarity
A new method for quantifying the organization of single bipolar electrograms recorded in the human atria during atrial fibrillation (AF) is presented. The algorithm relies on the comparison between pairs of local activation waves (LAWs) to estimate their morphological similarity, and returns a regularity index (/spl rho/) which measures the extent of repetitiveness over time of the detected activations. The database consisted of endocardial data from a multipolar basket catheter during AF and intraatrial recordings during atrial flutter. The index showed maximum regularity (/spl rho/=1) for all atrial flutter episodes and decreased significantly when increasing AF complexity as defined by W…
Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique
We present an approach, framed in information theory, to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system. The approach follows a sequential procedure for nonuniform embedding of multivariate time series, whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states. A corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure. The causal coupling is detected acc…
Assessing complexity and causality in heart period variability through a model-free data-driven multivariate approach
The aim of this study is to emphasize the importance of model-free data-driven mul- tivariate approaches in describing HP variability and cardiovascular control mechanisms responsible for inducing HP changes via modifications of different cardiovascular vari- ables such as SAP and RESP. The goal was achieved through the application, a previously proposed model-free data-driven multivariate framework devised to assess complexity and causality over a multivariate set composed by several, simultaneously recorded, car- diovascular variability series (Porta et al., 2014). The approach was applied to assess the complexity of the cardiac control, through the evaluation of the amount of irregularit…
Algorithms for the inference of causality in dynamic processes: Application to cardiovascular and cerebrovascular variability
This study faces the problem of causal inference in multivariate dynamic processes, with specific regard to the detection of instantaneous and time-lagged directed interactions. We point out the limitations of the traditional Granger causality analysis, showing that it leads to false detection of causality when instantaneous and time-lagged effects coexist in the process structure. Then, we propose an improved algorithm for causal inference that combines the Granger framework with the approach proposed by Pearl for the study of causality among multiple random variables. This new approach is compared with the traditional one in theoretical and simulated examples of interacting processes, sho…
An Information-Theoretic Framework to Map the Spatiotemporal Dynamics of the Scalp Electroencephalogram
We present the first application of the emerging framework of information dynamics to the characterization of the electroencephalography (EEG) activity. The framework provides entropy-based measures of information storage (self entropy, SE) and information transfer (joint transfer entropy (TE) and partial TE), which are applied here to detect complex dynamics of individual EEG sensors and causal interactions between different sensors. The measures are implemented according to a model-free and fully multivariate formulation of the framework, allowing the detection of nonlinear dynamics and direct links. Moreover, to deal with the issue of volume conduction, a compensation for instantaneous e…
Time-Varying Surrogate Data to Assess Nonlinearity in Nonstationary Time Series: Application to Heart Rate Variability
We propose a method to extend to time-varying (TV) systems the procedure for generating typical surrogate time series, in order to test the presence of nonlinear dynamics in potentially nonstationary signals. The method is based on fitting a TV autoregressive (AR) model to the original series and then regressing the model coefficients with random replacements of the model residuals to generate TV AR surrogate series. The proposed surrogate series were used in combination with a TV sample entropy (SE) discriminating statistic to assess nonlinearity in both simulated and experimental time series, in comparison with traditional time-invariant (TIV) surrogates combined with the TIV SE discrimin…
Mixed predictability and cross-validation to assess non-linear Granger causality in short cardiovascular variability series
A method to evaluate the direction and strength of causal interactions in bivariate cardiovascular and cardiorespiratory series is presented. The method is based on quantifying self and mixed predictability of the two series using nearest-neighbour local linear approximation. It returns two causal coupling indexes measuring the relative improvement in predictability along direct and reverse directions, and a directionality index indicating the preferential direction of interaction. The method was implemented through a cross-validation approach that allowed quantification of directionality without constraining the embedding of the series, and fully exploited the available data to maximise th…
Lag-specific transfer entropy as a tool to assess cardiovascular and cardiorespiratory information transfer
In the study of interacting physiological systems, model-free tools for time series analysis are fundamental to provide a proper description of how the coupling among systems arises from the multiple involved regulatory mechanisms. This study presents an approach which evaluates direction, magnitude, and exact timing of the information transfer between two time series belonging to a multivariate dataset. The approach performs a decomposition of the well-known transfer entropy (TE) which achieves 1) identifying, according to a lag-specific information-theoretic formulation of the concept of Granger causality, the set of time lags associated with significant information transfer, and 2) assig…
Need of causal analysis for assessing phase relationships in closed loop interacting cardiovascular variability series
The phase spectra obtained by the classical closed loop autoregressive model (2AR) and by an open loop autoregressive model (ARXAR) were compared to shed light on the need of introducing causality in the assessment of the delay between RR and arterial pressure oscillations. The reliability of the two approaches was tested in simulation and real data setting. In simulation, the coupling strength of a bivariate closed loop process was adjusted to obtain a range of working conditions from open to closed loop. In open loop condition, 2AR and ARXAR phases were comparable and in agreement with the imposed delay. In closed loop condition, ARXAR model returned the imposed delays, while 2AR showed a…
A stochastic approach for automatic registration and fusion of left atrial electroanatomic maps with 3D CT anatomical images.
The integration of electroanatomic maps with highly resolved computed tomography cardiac images plays an important role in the successful planning of the ablation procedure of arrhythmias. In this paper, we present and validate a fully-automated strategy for the registration and fusion of sparse, atrial endocardial electroanatomic maps (CARTO maps) with detailed left atrial (LA) anatomical reconstructions segmented from a pre-procedural MDCT scan. Registration is accomplished by a parameterized geometric transformation of the CARTO points and by a stochastic search of the best parameter set which minimizes the misalignment between transformed CARTO points and the LA surface. The subsequent …
Nonlinear effects of respiration on the crosstalk between cardiovascular and cerebrovascular control systems.
Cardiovascular and cerebrovascular regulatory systems are vital control mechanisms responsible for guaranteeing homeostasis and are affected by respiration. This work proposes the investigation of cardiovascular and cerebrovascular control systems and the nonlinear influences of respiration on both regulations through joint symbolic analysis (JSA), conditioned or unconditioned on respiration. Interactions between cardiovascular and cerebrovascular regulatory systems were evaluated as well by performing correlation analysis between JSA indexes describing the two control systems. Heart period, systolic and mean arterial pressure, mean cerebral blood flow velocity and respiration were acquired…
Assessing Causality in normal and impaired short-term cardiovascular regulation via nonlinear prediction methods
We investigated the ability of mutual nonlinear prediction methods to assess causal interactions in short-term cardiovascular variability during normal and impaired conditions. Directional interactions between heart period (RR interval of the ECG) and systolic arterial pressure (SAP) short-term variability series were quantified as the cross-predictability (CP) of one series given the other, and as the predictability improvement (PI) yielded by the inclusion of samples of one series into the prediction of the other series. Nonlinear prediction was performed through global approximation (GA), approximation with locally constant models (LA0) and approximation with locally linear models (LA1) …
An Automatic System for the Analysis and Classification of Human Atrial Fibrillation Patterns from Intracardiac Electrograms
This paper presents an automatic system for the analysis and classification of atrial fibrillation (AF) patterns from bipolar intracardiac signals. The system is made up of: 1) a feature- extraction module that defines and extracts a set of measures potentially useful for characterizing AF types on the basis of their degree of organization; 2) a feature-selection module (based on the Jeffries-Matusita distance and a branch and bound search algorithm) identifying the best subset of features for discriminating different AF types; and 3) a support vector machine technique-based classification module that automatically discriminates the AF types according to the Wells' criteria. The automatic s…
An integrated approach based on uniform quantization for the evaluation of complexity of short-term heart period variability: Application to 24 h Holter recordings in healthy and heart failure humans.
We propose an integrated approach based on uniform quantization over a small number of levels for the evaluation and characterization of complexity of a process. This approach integrates information-domain analysis based on entropy rate, local nonlinear prediction, and pattern classification based on symbolic analysis. Normalized and non-normalized indexes quantifying complexity over short data sequences (â¼300 samples) are derived. This approach provides a rule for deciding the optimal length of the patterns that may be worth considering and some suggestions about possible strategies to group patterns into a smaller number of families. The approach is applied to 24 h Holter recordings of …
Information Decomposition in Multivariate Systems: Definitions, Implementation and Application to Cardiovascular Networks
The continuously growing framework of information dynamics encompasses a set of tools, rooted in information theory and statistical physics, which allow to quantify different aspects of the statistical structure of multivariate processes reflecting the temporal dynamics of complex networks. Building on the most recent developments in this field, this work designs a complete approach to dissect the information carried by the target of a network of multiple interacting systems into the new information produced by the system, the information stored in the system, and the information transferred to it from the other systems; information storage and transfer are then further decomposed into amou…
Multivariate correlation measures reveal structure and strength of brain–body physiological networks at rest and during mental stress
In this work, we extend to the multivariate case the classical correlation analysis used in the field of network physiology to probe dynamic interactions between organ systems in the human body. To this end, we define different correlation-based measures of the multivariate interaction (MI) within and between the brain and body subnetworks of the human physiological network, represented, respectively, by the time series of delta, theta, alpha, and beta electroencephalographic (EEG) wave amplitudes, and of heart rate, respiration amplitude, and pulse arrival time (PAT) variability. MI is computed: (i) considering all variables in the two subnetworks to evaluate overall brain–body interaction…
Mutual nonlinear prediction of cardiovascular variability series: Comparison between exogenous and autoregressive exogenous models
A model-based approach to perform mutual nonlinear prediction of short cardiovascular variability series is presented. The approach is based on identifying exogenous (X) and autoregressive exogenous (ARX) models by K-nearest neighbors local linear approximation, and estimates the predictability of a series given the other as the squared correlation between original and predicted values of the series. The method was first tested on simulations reproducing different types of interaction between non-identical Henon maps, and then applied to heart rate (HR) and blood pressure (BP) variability series measured in healthy subjects at rest and after head-up tilt. Simulations showed that different c…
Bivariate nonlinear prediction to quantify the strength of complex dynamical interactions in short-term cardiovascular variability.
A nonlinear prediction method for investigating the dynamic interdependence between short length time series is presented. The method is a generalization to bivariate prediction of the univariate approach based on nearest neighbor local linear approximation. Given the input and output series x and y, the relationship between a pattern of samples of x and a synchronous sample of y was approximated with a linear polynomial whose coefficients were estimated from an equation system including the nearest neighbor patterns in x and the corresponding samples in y. To avoid overfitting and waste of data, the training and testing stages of the prediction were designed through a specific out-of-sampl…
Exploring directionality in spontaneous heart period and systolic pressure variability interactions in humans: implications in the evaluation of baroreflex gain
Although in physiological conditions RR interval and systolic arterial pressure (SAP) are likely to interact in a closed loop, the traditional cross-spectral analysis cannot distinguish feedback (FB) from feedforward (FF) influences. In this study, a causal approach was applied for calculating the coherence from SAP to RR ( Ks-r) and from RR to SAP ( Kr-s) and the gain and phase of the baroreflex transfer function. The method was applied, compared with the noncausal one, to RR and SAP series taken from 15 healthy young subjects in the supine position and after passive head-up tilt. For the low frequency (0.04–0.15 Hz) spectral component, the enhanced FF coupling ( Kr-s = 0.59 ± 0.21, signi…
Multiscale Granger causality
In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the dynamic complexity of individual processes at different time scales are well-established, multiscale analysis of directed interactions has never been formalized theoretically, and empirical evaluations are complicated by practical issues such as filtering and downsampling. Here we extend the very popular measure of Granger causality (GC), a prominent tool for assessing directed lagged interactions between joint processes, to quantify information transfer a…
Information-theoretic assessment of cardiovascular variability during postural and mental stress
This study was aimed at investigating the individual and combined effects of postural and mental stress on short-term cardiovascular regulation. To this end, we applied measures taken from the emerging framework of information dynamics on the beat-to-beat spontaneous variability of RR interval and systolic arterial pressure (SAP) measured from healthy subjects in the resting supine position and during the separate and simultaneous execution of experimental protocols performing head-up tilt (HUT) and mental arithmetics (MA). The information stored in RR interval variability, a measure inversely related to the complexity of the time series, increased significantly during HUT and HUT+MA compar…
Causal linear parametric model for baroreflex gain assessment in patients with recent myocardial infarction
Spectral and cross-spectral analysis of R-R interval and systolic arterial pressure (SAP) spontaneous fluctuations have been proposed for noninvasive evaluation of baroreflex sensitivity (BRS). However, results are not in good agreement with clinical measurements. In this study, a bivariate parametric autoregressive model with exogenous input (ARXAR model), able to divide the R-R variability into SAP-related and -unrelated parts, was used to quantify the gain (αARXAR) of the baroreflex regulatory mechanism. For performance assessing, two traditional noninvasive methods based on frequency domain analysis [spectral, baroreflex gain by autogressive model (αAR); cross-spectral, baroreflex gain…
An identifiable model to assess frequency-domain Granger causality in the presence of significant instantaneous interactions
We present a new approach for the investigation of Granger causality in the frequency domain by means of the partial directed coherence (PDC). The approach is based on the utilization of an extended multivariate autoregressive (MVAR) model, including instantaneous effects in addition to the lagged effects traditionally studied, to fit the observed multiple time series prior to PDC computation. Model identification is performed combining standard MVAR coefficient estimation with a recent technique for instantaneous causal modeling based on independent component analysis. The approach is first validated on simulated MVAR processes showing that, in the presence of instantaneous effects, only t…
Role of causality in the evaluation of coherence and transfer function between heart period and systolic pressure in humans
To elicit the effects of considering causality in the study of the interactions between RR interval and systolic pressure (SP) variability, the traditional noncausal cross-spectral analysis was compared with a causal method able to separate the two arms of the RR-SP regulatory loop. Estimates of coherence (K) and causal coherences from SP to RR (Ksr) and from RR to SP (Krs), and of noncausal (G) and causal (Gsr) baroreflex gain were evaluated at 0.1 Hz in 10 healthy young subjects in the supine position and after head-up tilt. While K was high in both conditions, at rest Ksr was significantly lower than Krs. After tilt, Ksr increased and Krs decreased significantly. With respect to G, Gsr w…
Evidence of unbalanced regulatory mechanism of heart rate and systolic pressure after acute myocardial infarction
The interactions between systolic arterial pressure (SAP) and R-R interval (RR) fluctuations after acute myocardial infarction (AMI) were investigated by measures of synchronization separating the feedback from the feedforward control and capturing both linear and nonlinear contributions. The causal synchronization, evaluating the ability of RR to predict SAP (χs/t) or vice versa (χt/s), and the global synchronization (χ) were estimated at rest and after head-up tilt in 35 post-AMI patients, 20 young and 12 old. Significance and nonlinearity of the coupling were assessed by surrogate data analysis. Tilting increased the number of young subjects in which RR-SAP link was significant (from 17…
Principal component analysis and cluster analysis for measuring the local organisation of human atrial fibrillation
The distribution of atrial electrogram types has been proposed to characterise human atrial fibrillation. The aim of this study was to provide computer procedures for evaluating the local organisation of intracardiac recordings during AF as an alternative to off-line manual classification. Principal components analysis (PCA) reduced the data set to a few representative activations, and cluster analysis (CA) measured the average dissimilarity between consecutive activations of an intracardiac signal. The data set consisted of 106 bipolar signals recorded on 11 patients during electrophysiological studies for catheter ablation. Performances of PCA and CA in distinguishing between organised (t…
Univariate and multivariate conditional entropy measures for the characterization of short-term cardiovascular complexity under physiological stress
Objective: A defining feature of physiological systems under the neuroautonomic regulation is their dynamical complexity. The most common approach to assess physiological complexity from short-term recordings, i.e. to compute the rate of entropy generation of an individual system by means of measures of conditional entropy (CE), does not consider that complexity may change when the investigated system is part of a network of physiological interactions. This study aims at extending the concept of short-term complexity towards the perspective of network physiology, defining multivariate CE measures whereby multiple physiological processes are accounted for in the computation of entropy rates.…
A framework for assessing frequency domain causality in physiological time series with instantaneous effects.
We present an approach for the quantification of directional relations in multiple time series exhibiting significant zero-lag interactions. To overcome the limitations of the traditional multivariate autoregressive (MVAR) modelling of multiple series, we introduce an extended MVAR (eMVAR) framework allowing either exclusive consideration of time-lagged effects according to the classic notion of Granger causality, or consideration of combined instantaneous and lagged effects according to an extended causality definition. The spectral representation of the eMVAR model is exploited to derive novel frequency domain causality measures that generalize to the case of instantaneous effects the kno…
Compensating for instantaneous signal mixing in transfer entropy analysis of neurobiological time series
The transfer entropy (TE) has recently emerged as a nonlinear model-free tool, framed in information theory, to detect directed interactions in coupled processes. Unfortunately, when applied to neurobiological time series TE is biased by signal cross-talk due to volume conduction. To compensate for this bias, in this study we introduce a modified TE measure which accounts for possible instantaneous effects between the analyzed time series. The new measure, denoted as compensated TE (cTE), is tested on simulated time series reproducing conditions typical of neuroscience applications, and on real magnetoencephalographic (MEG) multi-trial data measured during a visuo-tactile cognitive experime…
Feasibility of cuff-free measurement of systolic and diastolic arterial blood pressure
We validated a prototype cuff-free device for noninvasive estimation of blood pressure (BP). The system assumed a linear relation between BP values and the inverse of arterial blood pulse transit time, measured as time interval between the R wave on the electrocardiograph and the onset of the peripheral pulse wave on a finger plethysmogram. Thirty-three healthy subjects were analyzed at rest and during increasing stress exercise. To estimate subject-specific linear model parameters, the system was calibrated ad personam with reference to BP measures obtained by a cuff sphygmomanometer. High correlation values (R2= 0.89 and 0.78 for systolic and diastolic BP, respectively) and differences co…
Extended causal modeling to assess Partial Directed Coherence in multiple time series with significant instantaneous interactions.
The Partial Directed Coherence (PDC) and its generalized formulation (gPDC) are popular tools for investigating, in the frequency domain, the concept of Granger causality among multivariate (MV) time series. PDC and gPDC are formalized in terms of the coefficients of an MV autoregressive (MVAR) model which describes only the lagged effects among the time series and forsakes instantaneous effects. However, instantaneous effects are known to affect linear parametric modeling, and are likely to occur in experimental time series. In this study, we investigate the impact on the assessment of frequency domain causality of excluding instantaneous effects from the model underlying PDC evaluation. M…
Investigating the mechanisms of cardiovascular and cerebrovascular regulation in orthostatic syncope through an information decomposition strategy
Some previous evidence suggests that postural related syncope is associated with defective mechanisms of cerebrovascular (CB) and cardiovascular (CV) control. We characterized the information processing in short-term CB regulation, from the variability of mean cerebral blood flow velocity (CBFV) and mean arterial pressure (AP), and in CV regulation, from the variability of heart period (HP) and systolic AP (SAP), in ten young subjects developing orthostatic syncope in response to prolonged head-up tilt testing. We exploited a novel information-theoretic approach that decomposes the information associated with a variability series into three amounts: the information stored in the series, the…
Mutual nonlinear prediction as a tool to evaluate coupling strength and directionality in bivariate time series: Comparison among different strategies based on k nearest neighbors
We compare the different existing strategies of mutual nonlinear prediction regarding their ability to assess the coupling strength and directionality of the interactions in bivariate time series. Under the common framework of $k$-nearest neighbor local linear prediction, we test three approaches based on cross prediction, mixed prediction, and predictability improvement. The measures of interdependence provided by these approaches are first evaluated on short realizations of bivariate time series generated by coupled Henon models, investigating also the effects of noise. The usefulness of the three mutual nonlinear prediction schemes is then assessed in a common physiological application d…
Efficient Computation of Multiscale Entropy over Short Biomedical Time Series Based on Linear State-Space Models
The most common approach to assess the dynamical complexity of a time series across multiple temporal scales makes use of the multiscale entropy (MSE) and refined MSE (RMSE) measures. In spite of their popularity, MSE and RMSE lack an analytical framework allowing their calculation for known dynamic processes and cannot be reliably computed over short time series. To overcome these limitations, we propose a method to assess RMSE for autoregressive (AR) stochastic processes. The method makes use of linear state-space (SS) models to provide the multiscale parametric representation of an AR process observed at different time scales and exploits the SS parameters to quantify analytically the co…
Causal cross-spectral analysis of heart rate and blood pressure variability for describing the impairment of the cardiovascular control in neurally mediated syncope
A causal approach to the calculation of coherence and transfer function between systolic pressure (SP) and RR interval variability was applied in eight patients and eight control subjects during prolonged tilt test for investigating the impairment of cardiovascular control related to neurally mediated syncope. The causal analysis showed a depressed baroreflex regulation in resting patients, with reduced gain and increased latency from SP to RR, and a drop of the baroreflex coupling immediately before syncope. These findings, which were not elicited by traditional cross-spectral analysis, strongly suggest the use of the causal approach for the study of syncope mechanisms. © 2006 IEEE.
Information transfer and information modification to identify the structure of cardiovascular and cardiorespiratory networks
To fully elucidate the complex physiological mechanisms underlying the short-term autonomic regulation of heart period (H), systolic and diastolic arterial pressure (S, D) and respiratory (R) variability, the joint dynamics of these variables need to be explored using multivariate time series analysis. This study proposes the utilization of information-theoretic measures to measure causal interactions between nodes of the cardiovascular/cardiorespiratory network and to assess the nature (synergistic or redundant) of these directed interactions. Indexes of information transfer and information modification are extracted from the H, S, D and R series measured from healthy subjects in a resting…
Cardiovascular control and time domain granger causality: Insights from selective autonomic blockade
We studied causal relations among heart period (HP), systolic arterial pressure (SAP) and respiration (R) according to the definition of Granger causality in the time domain. Autonomic pharmacological challenges were used to alter the complexity of cardiovascular control. Atropine (AT), propranolol and clonidine (CL) were administered to block muscarinic receptors, β-adrenergic receptors and centrally sympathetic outflow, respectively. We found that: (i) at baseline, HP and SAP interacted in a closed loop with a dominant causal direction from HP to SAP; (ii) pharmacological blockades did not alter the bidirectional closed-loop interactions between HP and SAP, but AT reduced the dominance of…
Assessment of Granger causality by nonlinear model identification: application to short-term cardiovascular variability.
A method for assessing Granger causal relationships in bivariate time series, based on nonlinear autoregressive (NAR) and nonlinear autoregressive exogenous (NARX) models is presented. The method evaluates bilateral interactions between two time series by quantifying the predictability improvement (PI) of the output time series when the dynamics associated with the input time series are included, i.e., moving from NAR to NARX prediction. The NARX model identification was performed by the optimal parameter search (OPS) algorithm, and its results were compared to the least-squares method to determine the most appropriate method to be used for experimental data. The statistical significance of…
Nonlinear coupling is absent in acute myocardial patients but not healthy subjects.
We investigated whether autonomic nervous system imbalance imposed by pharmacological blockades and associated with acute myocardial infarction (AMI) is manifested as modifications of the nonlinear interactions in heart rate variability signal using a statistically based bispectrum method. The statistically based bispectrum method is an ideal approach for identifying nonlinear couplings in a system and overcomes the previous limitation of determining in an ad hoc way the presence of such interactions. Using the improved bispectrum method, we found significant nonlinear interactions in healthy young subjects, which were abolished by the administration of atropine but were still present afte…
Cerebrovascular and cardiovascular variability interactions investigated through conditional joint transfer entropy in subjects prone to postural syncope.
Objective: A model-based conditional transfer entropy approach was exploited to quantify the information transfer in cerebrovascular (CBV) and cardiovascular (CV) systems in subjects prone to develop postural syncope. Approach: Spontaneous beat-to-beat variations of mean cerebral blood flow velocity (MCBFV) derived from a transcranial Doppler device, heart period (HP) derived from surface electrocardiogram, mean arterial pressure (MAP) and systolic arterial pressure (SAP) derived from finger plethysmographic arterial pressure device were monitored at rest in supine position (REST) and during 60° head-up tilt (TILT) in 13 individuals (age mean ± standard deviation: 28 ± 9 years, min-max r…
Assessing directional interactions among multiple physiological time series: The role of instantaneous causality
This paper deals with the assessment of frequency domain causality in multivariate (MV) time series with significant instantaneous interactions. After providing different causality definitions, we introduce an extended MV autoregressive modeling approach whereby each definition is described in the time domain in terms of the model coefficients, and is quantified in the frequency domain by means of novel measures of directional connectivity. These measures are illustrated in a theoretical example showing how they reduce to known indexes when instantaneous causality is trivial, while they describe peculiar aspects of directional interaction in the presence of instantaneous causality. The appl…
Linear and nonlinear parametric model identification to assess granger causality in short-term cardiovascular interactions
We assessed directional relationships between short RR interval and systolic arterial pressure (SAP) variability series according to the concept of Granger causality. Causality was quantified as the predictability improvement (PI) of a time series obtained when samples of the other series were used for prediction, i.e. moving from autoregressive (AR) to AR exogenous (ARX) prediction. AR and ARX predictions were performed both by linear and nonlinear parametric models. The PIs of RR given SAP and of SAP given RR, measuring baroreflex and mechanical couplings, were calculated in 15 healthy subjects in the resting supine and upright tilt positions. Using nonlinear models we found a bilateral i…
A Multi-Variate Predictability Framework to Assess Invasive Cardiac Activity and Interactions during Atrial Fibrillation
Objective: This study introduces a predictability framework based on the concept of Granger causality (GC), in order to analyze the activity and interactions between different intracardiac sites during atrial fibrillation (AF). Methods: GC-based interactions were studied using a three-electrode analysis scheme with multi-variate autoregressive models of the involved preprocessed intracardiac signals. The method was evaluated in different scenarios covering simulations of complex atrial activity as well as endocardial signals acquired from patients. Results: The results illustrate the ability of the method to determine atrial rhythm complexity and to track and map propagation during AF. Conc…
Causal transfer function analysis to describe closed loop interactions between cardiovascular and cardiorespiratory variability signals
Although the concept of transfer function is intrinsically related to an input-output relationship, the traditional and widely used estimation method merges both feedback and feedforward interactions between the two analyzed signals. This limitation may endanger the reliability of transfer function analysis in biological systems characterized by closed loop interactions. In this study, a method for estimating the transfer function between closed loop interacting signals was proposed and validated in the field of cardiovascular and cardiorespiratory variability. The two analyzed signals x and y were described by a bivariate autoregressive model, and the causal transfer function from x to y w…
Information dynamics of brain-heart physiological networks during sleep
This study proposes an integrated approach, framed in the emerging fields of network physiology and information dynamics, for the quantitative analysis of brain-heart interaction networks during sleep. With this approach, the time series of cardiac vagal autonomic activity and brain wave activities measured respectively as the normalized high frequency component of heart rate variability and the EEG power in the δ, θ, Ï, and β bands, are considered as realizations of the stochastic processes describing the dynamics of the heart system and of different brain sub-systems. Entropy-based measures are exploited to quantify the predictive information carried by each (sub)system, and to dissec…
Measuring postural-related changes of spontaneous baroreflex sensitivity after repeated long-duration diving: Frequency domain approaches
Sustained water immersion is thought to modulate orthostatic tolerance to an extent dependent on the duration and repetition over consecutive days of the diving sessions. We tested this hypothesis investigating in ten healthy subjects the potential changes in the cardiovascular response to head-up tilt induced by single and multiple resting air dives. Parametric cross-spectral analysis of spontaneous RR interval and systolic arterial pressure variability was performed in three experimental sessions: before diving (BD), after single 6-hour dive (ASD), and after multiple 6-hour dives (AMD, 5 consecutive days with 18-hour surface interval). From this analysis, baroreflex sensitivity (BRS) was …
Investigating the level of significance of the coherence function in cardiovascular variability analysis
Although the presence of significant coupling between cardiovascular variability series is usually verified according to the threshold value of 0.5 in the coherence function (CF), spectral estimator parameters should also be considered. In this study, the surrogate data technique was introduced to define the level of significance of the CF. The proposed method determined a frequency-dependent threshold over which the hypothesis of zero coherence was rejected. The weighted covariance method and the autoregressive method were used to estimate the CF on simulated series with different degrees of linear coupling and on real cardiovascular data. The threshold was dependent on the type and parame…
Multilevel assessment of mental stress via network physiology paradigm using consumer wearable devices
Mental stress is a physiological condition that has a strong negative impact on the quality of life, affecting both the physical and the mental health. For such a reason, accurate measurements of stress level can be helpful to provide mechanisms for prevention and treatment. This paper proposes a procedure for the classification of different mental stress levels by using physiological signals provided by low invasive wearable devices. 17 healthy volunteers participated in this study. Three different mental states were elicited in them: a resting condition, a stressful cognitive state, and a sustained attention task. The acquired physiological signals were: a one lead electrocardiogram (ECG)…
Isolation of the left atrial surface from cardiac multi-detector CT images based on marker controlled watershed segmentation
The delineation of left atrium (LA) and pulmonary veins (PVs) anatomy from high resolution images holds importance for atrial fibrillation (AF) investigation and treatment. In this study, a semiautomatic segmentation procedure for LA and PVs inner surface from contrast enhanced CT data was developed. The procedure consists of a three dimensional marker controlled watershed segmentation applied to the external morphological gradient, followed by variable threshold surface extraction from the original intensity image. A preliminary anisotropic non-linear filtering was implemented to improve the S/N ratio of CT images. The performance of segmentation was evaluated on cardiac CT scans of 12 AF …
Information Transfer in Linear Multivariate Processes Assessed through Penalized Regression Techniques: Validation and Application to Physiological Networks
The framework of information dynamics allows the dissection of the information processed in a network of multiple interacting dynamical systems into meaningful elements of computation that quantify the information generated in a target system, stored in it, transferred to it from one or more source systems, and modified in a synergistic or redundant way. The concepts of information transfer and modification have been recently formulated in the context of linear parametric modeling of vector stochastic processes, linking them to the notion of Granger causality and providing efficient tools for their computation based on the state&ndash
Information-theoretic assessment of cardiovascular-brain networks during sleep
This study was aimed at detecting the structure of the physiological network underlying the regulation of the cardiovascular and brain systems during normal sleep. To this end, we measured from the polysomnographic recordings of 10 healthy subjects the normalized spectral power of heart rate variability in the high frequency band (HF) and the EEG power in the δ, θ, α, σ, and β bands. Then, the causal statistical dependencies within and between these six time series were assessed in terms of internal information (conditional self entropy, CSE) and information transfer (transfer entropy, TE) computed via a linear method exploiting multiple regression models and a nonlinear method combining ne…
Compensated transfer entropy as a tool for reliably estimating information transfer in physiological time series
We present a framework for the estimation of transfer entropy (TE) under the conditions typical of physiological system analysis, featuring short multivariate time series and the presence of instantaneous causality (IC). The framework is based on recognizing that TE can be interpreted as the difference between two conditional entropy (CE) terms, and builds on an efficient CE estimator that compensates for the bias occurring for high dimensional conditioning vectors and follows a sequential embedding procedure whereby the conditioning vectors are formed progressively according to a criterion for CE minimization. The issue of IC is faced accounting for zero-lag interactions according to two a…
Redundant and synergistic information transfer in cardiovascular and cardiorespiratory variability
In the framework of information dynamics, new tools are emerging which allow one to quantify how the information provided by two source processes about a target process results from the contribution of each source and from the interaction between the sources. We present the first implementation of these tools in the assessment of short-term cardiovascular and cardiorespiratory variability, by introducing two strategies for the decomposition of the information transferred to heart period (HP) variability from systolic arterial pressure (SAP) and respiration flow (RF) variability. Several measures based on the notion of transfer entropy (TE) are defined to quantify joint, individual and redun…
Granger causality analysis of sleep brain-heart interactions
We studied the networks of Granger causality (GC) between the time series of cardiac vagal autonomic activity and brain wave activities, measured respectively as the normalized high frequency (HF) component of heart rate variability and EEG power in the δ, θ, α, Ï, β bands, computed in 10 healthy subjects during sleep. GC analysis was performed by vector autoregressive modeling, and significance of each link in the network was assessed using F-statistics. The whole-night analysis revealed the existence of a fully connected network of brain-heart and brain-brain interactions, with the à EEG power acting as a hub which conveys the largest number of GC links between the heart and brain n…
Assessment Of Driving Stress Through SVM And KNN Classifiers On Multi-Domain Physiological Data
We propose an objective stress assessment method based on the extraction of features from physiological time series and their classification using Support Vector Machine and K-Nearest Neighbors algorithms. For this purpose, we used an open dataset consisting of multiparametric physiological signals (electrocardiogram, electromyogram, galvanic skin response and breath signal) obtained during the execution of a driving route within the city of Boston with restful, highway and city driving periods indicative of three different stress states. To predict the driver stress level, 21 features were extracted from 122 chunks of raw signals and were subsequently managed by classification algorithms. …
Robust estimation of partial directed coherence by the vector optimal parameter search algorithm
We propose a method for the accurate estimation of Partial Directed Coherence (PDC) from multichannel time series. The method is based on multivariate vector autoregressive (MVAR) model identification performed through the recently proposed Vector Optimal Parameter Search (VOPS) algorithm. Using Monte Carlo simulations generated by different MVAR models, the proposed VOPS algorithm is compared with the traditional Vector Least Squares (VLS) identification method. We show that the VOPS provides more accurate PDC estimates than the VLS (either overall and single-arc errors) in presence of interactions with long delays and missing terms, and for noisy multichannel time series. ©2009 IEEE.
Linear and non-linear brain-heart and brain-brain interactions during sleep.
In this study, the physiological networks underlying the joint modulation of the parasympathetic component of heart rate variability (HRV) and of the different electroencephalographic (EEG) rhythms during sleep were assessed using two popular measures of directed interaction in multivariate time series, namely Granger causality (GC) and transfer entropy (TE). Time series representative of cardiac and brain activities were obtained in 10 young healthy subjects as the normalized high frequency (HF) component of HRV and EEG power in the δ, θ, α, Ï, and β bands, measured during the whole duration of sleep. The magnitude and statistical significance of GC and TE were evaluated between each …
Small-sample characterization of stochastic approximation staircases in forced-choice adaptive threshold estimation
Despite the widespread use of up—down staircases in adaptive threshold estimation, their efficiency and usability in forced-choice experiments has been recently debated. In this study, simulation techniques were used to determine the small-sample convergence properties of stochastic approximation (SA) staircases as a function of several experimental parameters. We found that satisfying some general requirements (use of the accelerated SA algorithm, clear suprathreshold initial stimulus intensity, large initial step size) the convergence was accurate independently of the spread of the underlying psychometric function. SA staircases were also reliable for targeting percent-correct levels far …
Quantitative assessment of regularity and synchronization of intracardiac recordings during human atrial fibrillation
This study proposes the morphology-based evaluation of the regularity (R) and the synchronization (S) of intra-atrial electrograms acquired during atrial fibrillation (AF). R is defined as the degree of repetitiveness over time of the shapes of the activation waves detected in single atrial recordings. S accounts for the simultaneous presence of morphologically similar activation waves in two atrial electrograms, and for the dispersion of the propagation delays between the two sites. Both R and S resulted unitary for normal sinus rhythm and decreased significantly moving from atrial flutter (R=0.93, S=0.88) to AF of increasing complexity class (type I AF: R=0.75, S=0.66; type II AF: R=0.32,…
Morphology-based measurement of activation time in human atrial fibrillation
The measurement of the activation time is crucial to allow the correct automatic analysis and classification of intracardiac electrograms recorded in the human atria during atrial fibrillation (AF). This study proposes a method which accounts for the morphology of bipolar signals. After ventricular artifact removal and activation wave recognition, the fiducial point of the activation wave was set at its local barycentre (LB). The method was tested on a set of 30 AF bipolar recordings of increasing complexity class; its performance was compared with that of the traditional methods of maximum peak (MP) or maximum slope (MS) estimation, taking the manual measurements performed by an expert car…
Extended Granger causality: a new tool to identify the structure of physiological networks.
Granger causality (GC) is a very popular tool for assessing the presence of directional interactions between two time series of a multivariate data set. In its original formulation, GC does not account for zero-lag correlations possibly existing between the observed time series. In the present study we compare the GC with a novel measure, termed extended GC (eGC), able to capture instantaneous causal relationships. We present a two-step procedure for the practical estimation of eGC based on first detecting the existence of zero-lag correlations, and then assigning them to one of the two possible causal directions using pairwise measures of non-Gaussianity. The proposed method was validated …
Surrogate data approaches to assess the significance of directed coherence: Application to EEG activity propagation
This paper addresses the topic of evaluating the significance of frequency domain measures of causal coupling in multivariate time series through generation of surrogate data. The considered approaches are the traditional Fourier Transform (FT) algorithm and a new causal FT (CFT) algorithm for surrogate data generation. Both algorithms preserve the FT modulus of the original series; differences are in the phase relationships, that are completely destroyed for FT surrogates and imposed after switching off the link over the considered causal direction for CFT surrogates. The ability of the algorithms to assess causality in the frequency domain was tested using the directed coherence as discri…
k-Nearest neighbour local linear prediction of scalp EEG activity during intermittent photic stimulation
The characterization of the EEG response to photic stimulation (PS) is an important issue with significant clinical relevance. This study aims to quantify and map the complexity of the EEG during PS, where complexity is measured as the degree of unpredictability resulting from local linear prediction. EEG activity was recorded with eyes closed (EC) and eyes open (EO) during resting and PS at 5, 10, and 15. Hz in a group of 30 healthy subjects and in a case-report of a patient suffering from cerebral ischemia. The mean squared prediction error (MSPE) resulting from k-nearest neighbour local linear prediction was calculated in each condition as an index of EEG unpredictability. The linear or …
A method for the time-varying nonlinear prediction of complex nonstationary biomedical signals
A method to perform time-varying (TV) nonlinear prediction of biomedical signals in the presence of nonstationarity is presented in this paper. The method is based on identification of TV autoregressive models through expansion of the TV coefficients onto a set of basis functions and on k -nearest neighbor local linear approximation to perform nonlinear prediction. The approach provides reasonable nonlinear prediction even for TV deterministic chaotic signals, which has been a daunting task to date. Moreover, the method is used in conjunction with a TV surrogate method to provide statistical validation that the presence of nonlinearity is not due to nonstationarity itself. The approach is t…
Experimental approach for testing the uncoupling between cardiovascular variability series
In cardiovascular variability analysis, the significance of the coupling between two series is commonly assessed by defining a zero level on the magnitude-squared coherence (MSC). Although the use of the conventional value of 0.5 does not consider the dependence of MSC estimates on the analysis parameters, a theoretical threshold Tt is available only for the weighted covariance (WC) estimator. In this study, an experimental threshold for zero coherence Te was derived by a statistical test from the sampling distribution of MSC estimated on completely uncoupled time series. MSC was estimated by the WC method (Parzen window, spectral bandwidth B = 0.015, 0.02, 0.025, 0.03 Hz) and by the parame…
Registration and fusion of segmented left atrium CT images with CARTO electrical maps for the ablative treatment of atrial fibrillation
This study aims to extract the interior surface of the left atrium (LA) and pulmonary veins (PVs) from threedimensional tomographic data and to integrate it with LA CARTO electrical maps. The separation of LA and PVs from other overlapping structures of the heart was performed processing 3D CT data by marker-controlled watershed segmentation and surface extraction. CARTO maps were then registered on the L A internal surface by a stochastic optimization algorithm based on simulated annealing. The residual registration error resulted inferior to 3 mm. The integration between electrophysiological and high resolved anatomic information of LA results feasible and may constitute a significant sup…
Investigating cardiac and respiratory determinants of heart rate variability in an information-theoretic framework.
This study was aimed at comparing two alternative information-theoretic approaches for the combined analysis of heart rate variability (HRV) and respiration variability (RV). The approaches decompose the predictive information about HRV in two terms, quantifying respectively the information stored into HRV and that transferred to HRV from RV. Storage and transfer were assessed by the popular self entropy (SE) and transfer entropy (TE) measures, as well as by the alternative conditional SE (cSE) and cross entropy (CE) measures. The comparison was performed at a theoretical level, computing the exact values of the four measures for simulated cardiorespiratory dynamics, and on real data, estim…
Mutual Information Analysis of Brain-Body Interactions during different Levels of Mental stress
In this work, we analyze brain-heart interactions during different mental states computing mutual information (MI) between the dynamic activity of different physiological systems. In 18 healthy subjects monitored in a relaxed resting state and during a mental arithmetic and a serious game task, multichannel EEG, one lead ECG, respiration and blood volume pulse were collected via wireless non-invasive biosensors. From these signals, synchronous 300-second time series were extracted measuring brain activity via the δ, θ, α, and β EEG power, and activity of the body district via the ECG R-R interval η, the respiratory amplitude ϱ and the pulse arrival time π. MI was computed using a linear est…
Non-uniform multivariate embedding to assess the information transfer in cardiovascular and cardiorespiratory variability series
The complexity of the short-term cardiovascular control prompts for the introduction of multivariate (MV) nonlinear time series analysis methods to assess directional interactions reflecting the underlying regulatory mechanisms. This study introduces a new approach for the detection of nonlinear Granger causality in MV time series, based on embedding the series by a sequential, non-uniform procedure, and on estimating the information flow from one series to another by means of the corrected conditional entropy. The approach is validated on short realizations of linear stochastic and nonlinear deterministic processes, and then evaluated on heart period, systolic arterial pressure and respira…
Multiscale analysis of information dynamics for linear multivariate processes.
In the study of complex physical and physiological systems represented by multivariate time series, an issue of great interest is the description of the system dynamics over a range of different temporal scales. While information-theoretic approaches to the multiscale analysis of complex dynamics are being increasingly used, the theoretical properties of the applied measures are poorly understood. This study introduces for the first time a framework for the analytical computation of information dynamics for linear multivariate stochastic processes explored at different time scales. After showing that the multiscale processing of a vector autoregressive (VAR) process introduces a moving aver…
Cardiovascular and respiratory variability during orthostatic and mental stress: A comparison of entropy estimators
The aim of this study is to characterize cardiovascular and respiratory signals during orthostatic and mental stress as reflected in indices of entropy and complexity, providing a comparison between the performance of different estimators. To this end, the heart rate variability, systolic blood pressure, diastolic blood pressure and respiration time series were extracted from the recordings of 61 healthy volunteers undergoing a protocol consisting of supine rest, head-up tilt test and mental arithmetic task. The analysis was performed in the information domain using measures of entropy and conditional entropy, estimated through model-based (linear) and model-free (binning, nearest neighbor)…
Assessing Frequency Domain Causality in Cardiovascular Time Series with Instantaneous Interactions
Summary Background: The partial directed coherence (PDC) is commonly used to assess in the frequency domain the existence of causal relations between two time series measured in conjunction with a set of other time series. Although the multivariate autoregressive (MVAR) model traditionally used for PDC computation accounts only for lagged effects, instantaneous effects cannot be neglected in the analysis of cardiovascular time series. Objectives: We propose the utilization of an extended MVAR model for PDC computation, in order to improve the evaluation of frequency domain causality in the presence of zero-lag correlations among multivariate time series. Methods: A procedure for the identif…
Minimally Invasive Assessment of Mental Stress based on Wearable Wireless Physiological Sensors and Multivariate Biosignal Processing
The development of connected health technologies for the continuous monitoring of the psychophysical state of individuals performing daily life activities requires the aggregation of non-intrusive sensors and the availability of methods and algorithms for extracting the relevant physiological information. The present study proposes an integrated approach for the objective assessment of mental stress which combines wirelessly connected low invasive biosensors with multivariate physiological time series analysis. In a group of 18 healthy subjects monitored in a relaxed resting state and during two experimental conditions inducing mental stress and sustained attention (respectively, mental ari…
Multivariate Frequency Domain Analysis of Causal Interactions in Physiological Time Series
A common way of obtaining information about a physiological system is to measure one or more signals from the system, consider their temporal evolution in the form of numerical time series, and obtain quantitative indexes through the application of time series analysis techniques. While historical approaches to time series analysis were addressed to the study of single signals, recent advances have made it possible to study collectively the behavior of several signals measured simultaneously from the considered system. In fact, multivariate (MV) time series analysis is nowadays extensively used to characterize interdependencies among multiple signals collected from dynamical physiological s…
Investigating cardiovascular and cerebrovascular variability in postural syncope by means of extended Granger causality
The patterns of Granger causality (GC) between heart period (HP), mean arterial pressure (AP) and cerebral blood flow velocity (FV) were investigated in ten subjects with postural related syncope (PRS). The classic GC measure based on vector autoregressive (VAR) modeling was compared with a novel extended GC (eGC) measure derived from VAR models incorporating instantaneous causal effects among the series. The analysis was performed in the supine and in the upright position during early (ET) and late (LT, close to presyncope) epochs of head-up tilt. Moving from ET to LT, both GC and eGC decreased from AP to HP, and increased from AP to FV, reflecting baroreflex impairment and loss of cerebra…
Comparison of Methods for the Assessment of Nonlinearity in Short-Term Heart Rate Variability under different Physiopathological States
Despite the widespread diffusion of nonlinear methods for heart rate variability (HRV) analysis, the presence and the extent to which nonlinear dynamics contribute to short-term HRV are still controversial. This work aims at testing the hypothesis that different types of nonlinearity can be observed in HRV depending on the method adopted and on the physiopathological state. Two entropy-based measures of time series complexity (normalized complexity index, NCI) and regularity (information storage, IS), and a measure quantifying deviations from linear correlations in a time series (Gaussian linear contrast, GLC), are applied to short HRV recordings obtained in young (Y) and old (O) healthy su…
Evaluation of a nonlinear prediction algorithm quantifying regularity, synchronization and directionality in short cardiovascular variability series
An unifying approach evaluating complex dynamics and dynamical interactions in short bivariate time series is presented. The method performs nearest neighbor local linear prediction to estimate regularity, synchronization and directionality of two interacting time series. It was implemented through a specific cross-validation procedure which allowed an unconstrained embedding of the series and a full exploitation of the available data to maximize the accuracy of prediction. The approach was evaluated by simulations of stochastic (autoregressive processes) and deterministic (Henon maps) models in which uncoupled, unidirectionally coupled and bidirectionally coupled dynamics were generated. T…
Measuring Connectivity in Linear Multivariate Processes: Definitions, Interpretation, and Practical Analysis
This tutorial paper introduces a common framework for the evaluation of widely used frequency-domain measures of coupling (coherence, partial coherence) and causality (directed coherence, partial directed coherence) from the parametric representation of linear multivariate (MV) processes. After providing a comprehensive time-domain definition of the various forms of connectivity observed in MV processes, we particularize them to MV autoregressive (MVAR) processes and derive the corresponding frequency-domain measures. Then, we discuss the theoretical interpretation of these MVAR-based connectivity measures, showing that each of them reflects a specific time-domain connectivity definition an…
Comparison of frequency domain measures based on spectral decomposition for spontaneous baroreflex sensitivity assessment after Acute Myocardial Infarction
Abstract The objective of this study is to present a new method to assess in the frequency domain the directed interactions between the spontaneous variability of systolic arterial pressure (SAP) and heart period (HP) from their linear model representation, and to apply it for studying the baroreflex control of arterial pressure in healthy physiological states and after acute myocardial infarction (AMI). The method is based on pole decomposition of the model transfer function and on the following evaluation of causal measures of coupling and gain from the poles associated to low frequency (0.04−0.15 Hz) oscillatory components. It is compared with traditional non-causal approaches for the sp…
Exploring causal interactions between blood pressure and RR interval at the respiratory frequency
The mechanisms underlying the relationship between RR interval and systolic arterial pressure (SAP) variability at the respiratory frequency are still object of discussion. In this study, the information on directionality provided by causal cross-spectral analysis was exploited to infer possible influences of respiration on cardiovascular parameters variability. The ability of causal analysis to account for directionality in RR-SAP interrelationships in presence of respiratory exogenous effects was first tested on model simulations. Hence, real data measured on healthy subjects during spontaneous and paced breathing at 0.25 Hz were analysed. The results obtained in real data were consistent…
Information Decomposition: A Tool to Dissect Cardiovascular and Cardiorespiratory Complexity
This chapter reports some recent developments of information-theoretic concepts applied to the description of coupled dynamical systems, which allow to decompose the entropy of an assigned target system into components reflecting the information stored in the system and the information transferred to it from the other systems, as well as the nature (synergistic or redundant) of the information transferred to the target. The decomposition leads to well-defined measures of information dynamics which in the chapter will be defined theoretically, computed in simulations of linear Gaussian systems and implemented in practice through the application to heart period, arterial pressure and respirat…
Detecting nonlinear causal interactions between dynamical systems by non-uniform embedding of multiple time series.
This study introduces a new approach for the detection of nonlinear Granger causality between dynamical systems. The approach is based on embedding the multivariate (MV) time series measured from the systems X and Y by means of a sequential, non-uniform procedure, and on using the corrected conditional entropy (CCE) as unpredictability measure. The causal coupling from X to Y is quantified as the relative decrease of CCE measured after allowing the series of X to enter the embedding procedure for the description of Y. The ability of the approach to quantify nonlinear causality is assessed on MV time series measured from simulated dynamical systems with unidirectional coupling (the Rössler-…
Bridging the gap between the development of advanced biomedical signal processing tools and clinical practice
In the last twenty years the eld of the biomedical signal processing has known an upsurge, as witnessed by the progressively increasing number of peer-review international journals and sessions in biomedical meetings.
Effect of age on complexity and causality of the cardiovascular control: comparison between model-based and model-free approaches.
The proposed approach evaluates complexity of the cardiovascular control and causality among cardiovascular regulatory mechanisms from spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiration (RESP). It relies on construction of a multivariate embedding space, optimization of the embedding dimension and a procedure allowing the selection of the components most suitable to form the multivariate embedding space. Moreover, it allows the comparison between linear model-based (MB) and nonlinear model-free (MF) techniques and between MF approaches exploiting local predictability (LP) and conditional entropy (CE). The framework was applied to study age-related…
Noninvasive assessment of baroreflex sensitivity in post-MI patients by an open loop parametric model of RR-systolic pressure interactions
Noninvasive evaluation of baroreflex sensitivity is considered an important goal for diagnosis and prognosis in post-MI patients. Methodological approach and physiological measure conditions may be the main causes for the differences found with respect to the standard Phenylephrine test. In this study, three linear parametric models, describing variability and mutual interactions of RR interval and systolic arterial pressure (SAP), were compared in relation to their ability to quantify baroreflex gain, using the Phenylephrine test index (Phe/sub BRS/) as reference. By monovariate autoregressive (AR) model, bivariate AR model and open loop ARXAR model, specific gain indexes (/spl alpha//sub …
Quantifying the complexity of short-term heart period variability through K nearest neighbor local linear prediction
The complexity of short-term heart period (HP) variability was quantified exploiting the paradigm that associates the degree of unpredictability of a time series to its dynamical complexity. Complexity was assessed through k-nearest neighbor local linear prediction. A proper selection of the parameter k allowed us to perform either linear or nonlinear prediction, and the comparison of the two approaches to infer the presence of nonlinear dynamics. The method was validated on simulations reproducing linear and nonlinear time series with varying levels of predictability. It was then applied to HP variability series measured from healthy subjects during head-up tilt test, showing that short-te…
Multivariate EEG spectral analysis evidences the functional link between motor and visual cortex during integrative sensorimotor tasks
The identification of the networks connecting brain areas and the understanding of their role in executing complex tasks is a crucial issue in cognitive neuroscience. In this study, specific visuomotor tasks were devised to reveal the functional network underlying the cooperation process between visual and motor regions. Electroencephalography (EEG) data were recorded from twelve healthy subjects during a combined visuomotor task, which integrated precise grip motor commands with sensory visual feedback (VM). This condition was compared with control tasks involving pure motor action (M), pure visual perception (V) and visuomotor performance without feedback (V + M). Multivariate parametric …
Synchronization index for quantifying nonlinear causal coupling between RR interval and systolic arterial pressure after myocardial infarction
The analysis of nonlinear couplings among cardiovascular variability series can improve the knowledge of the cardioregulatory mechanism and help to understand how it can be affected by pathologies. In this study, the influences of acute myocardial infarction (AMI) on the causal relationships between the heart period and the arterial pressure were investigated by a nonlinear dynamic approach based on the corrected cross-conditional entropy. Whereas the global synchronization index did not differentiate the post-AMI patients from the young and old control groups, the causal indexes evidenced the impairment of the baroreflex control and showed an increase of the mechanical driving of the RR in…
Quantifying the contribution of arm postural tremor to the outcome of goal-directed pointing task by displacement measures.
A method for quantifying the outcome of goal-directed postural pointing was presented and used for relating the tremor output to the oscillations of single arm landmarks. The displacement of reflective markers placed on shoulder, upper arm, forearm, and hand were measured by an optoelectronic motion capture system in nine subjects holding a laser penlight pointed at a target. The high signal-to-noise ratio of the measured displacement series (from 7:1 for shoulder marker to 30:1 for hand marker) demonstrated the feasibility of the proposed system to carry out tremor analysis. The track of the laser emission on the target, reconstructed from penlight displacements, was studied as the outcome…
Spectral decomposition of RR-variability obtained by an open loop parametric model for the diagnosis of neuromediate syncope
The role of the cardiovascular regulatory mechanism in patients with neuromediate syncope (NS) is poorly understood. The aim of this study was to accomplish continuous non-invasive analysis of the baroreflex mechanism in patients during a head-tip tilt-table test (HTT) using an open-loop autoregressive model with exogenous input. The model describes the causal dependence of the RR interval on the systolic arterial pressure (SAP) variability. Thus, RR variability results as the linear composition of SAP-dependent (Pdep) and SAP-independent parts of the RR power (P). Further, the model allows the estimation of the baroreflex gain using the modulus of the transfer function (G) from SAP to RR i…
Testing Frequency-Domain Causality in Multivariate Time Series
We introduce a new hypothesis-testing framework, based on surrogate data generation, to assess in the frequency domain, the concept of causality among multivariate (MV) time series. The approach extends the traditional Fourier transform (FT) method for generating surrogate data in a MV process and adapts it to the specific issue of causality. It generates causal FT (CFT) surrogates with FT modulus taken from the original series, and FT phase taken from a set of series with causal interactions set to zero over the direction of interest and preserved over all other directions. Two different zero-setting procedures, acting on the parameters of a MV autoregressive (MVAR) model fitted on the ori…
Mechanisms of causal interaction between short-term RR interval and systolic arterial pressure oscillations during orthostatic challenge
The transition from the supine to the upright position requires a reorganization of the mechanisms of cardiovascular control that, if not properly accomplished, may lead to neurally mediated syncope. We investigated how the patterns of causality between systolic arterial pressure (SAP) and cardiac RR interval were modified by prolonged head-up tilt using a novel nonlinear approach based on corrected conditional entropy (CCE) compared with the standard approach exploiting the cross-correlation function (CCF). Measures of coupling strength and delay of the causal interactions from SAP to RR and from RR to SAP were obtained in 10 patients with recurrent, neurally mediated syncope (RNMS) and 10…
Surrogate Data Analysis for Assessing the Significance of the Coherence Function
In cardiovascular variability analysis, the significance of the coupling between two time series is commonly assessed by setting a threshold level in the coherence function. While traditionally used statistical tests consider only the parameters of the adopted estimator, the required zero-coherence level may be affected by some features of the observed series. In this study, three procedures, based on the generation of surrogate series sharing given properties with the original but being structurally uncoupled, were considered: independent identically distributed (IID), Fourier transform (FT), and autoregressive (AR). IID surrogates maintained the distribution of the original series, while …
Quantifying changes in EEG complexity induced by photic stimulation.
Summary Objectives: This study aims to characterize EEG complexity, measured as the prediction error resulting from nonlinear prediction, in healthy humans during photic stimulation. Methods: EEGs were recorded from 15 subjects with eyes closed (EC) and eyes open (EO), during the baseline condition and during stroboscopic photic stimulation (PS) at 5, 10, and 15 Hz. The mean squared prediction error (MSPE) resulting from nearest neighbor local linear prediction was taken as complexity index. Complexity maps were generated interpolating the MSPE index over a schematic scalp representation. Results: Statistical analysis revealed that: i) EEG shows good predictability in all conditions and see…
Parametric and nonparametric methods to generate time-varying surrogate data.
We present both nonparametric and parametric approaches to generating time-varying surrogate data. Nonparametric and parametric approaches are based on the use of the short-time Fourier transform and a time-varying autoregressive model, respectively. Time-varying surrogate data (TVSD) can be used to determine the statistical significance of the linear and nonlinear coherence function estimates. Two advantages of the TVSD are that it keeps one from having to make an arbitrary decision about the significance of the coherence value, and it properly takes into account statistical significance levels, which may change with time. Our simulation examples and experimental results on blood pressure …
Decomposing the transfer entropy to quantify lag-specific Granger causality in cardiovascular variability.
We present a modification of the well known transfer entropy (TE) which makes it able to detect, besides the direction and strength of the information transfer between coupled processes, its exact timing. The approach follows a decomposition strategy which identifies--according to a lag-specific formulation of the concept of Granger causality--the set of time delays carrying significant information, and then assigns to each of these delays an amount of information transfer such that the total contribution yields the overall TE. We propose also a procedure for the practical estimation from time series data of the relevant delays and lag-specific TE in both bivariate and multivariate settings…
Studying brain visuo-tactile integration through cross-spectral analysis of human MEG recordings
An important aim in cognitive neuroscience is to identify the networks connecting different brain areas and their role in executing complex tasks. In this study, visuo-tactile tasks were employed to assess the functional correlation underlying the cooperation process between visual and tactile regions. MEG data were recorded from eight healthy subjects while performing a visual, a tactile, and a visuo-tactile task. To define regions of interest (ROIs), event-related fields (ERFs) were estimated from MEG data related to visual and tactile areas. The ten channels with the highest increase in ERF variance, moving from rest to task, were selected. Cross-spectral analysis was then performed to a…
Estimating the decomposition of predictive information in multivariate systems
In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of co…
Conditional Self-Entropy and Conditional Joint Transfer Entropy in Heart Period Variability during Graded Postural Challenge.
Self-entropy (SE) and transfer entropy (TE) are widely utilized in biomedical signal processing to assess the information stored into a system and transferred from a source to a destination respectively. The study proposes a more specific definition of the SE, namely the conditional SE (CSE), and a more flexible definition of the TE based on joint TE (JTE), namely the conditional JTE (CJTE), for the analysis of information dynamics in multivariate time series. In a protocol evoking a gradual sympathetic activation and vagal withdrawal proportional to the magnitude of the orthostatic stimulus, such as the graded head-up tilt, we extracted the beat-to-beat spontaneous variability of heart per…
Quantitative assessment of synchronization during atrial fibrillation by Shannon Entropy characterization of propagation delays
This study introduced a new method for the quantification of the synchronization (S) and the causal verse of activation (S12) in couples of atrial electrograms recorded during atrial fibrillation (AF). The synchronization indexes S and S12 relied on the measure of the propagation delays between coupled activation times in two atrial signals and on the characterization of their dispersion by Shannon-Entropy (SE). S and S12 were validated both on simulated activation time series and endocavitary signals in patients. In simulation, S and S12 were equal to 1 for propagation of one single wavefront in a fully excitable tissue, while they decreased for reentries in partially excitable tissue (S =…
Model-Based Transfer Entropy Analysis of Brain-Body Interactions with Penalized regression techniques
The human body can be seen as a functional network depicting the dynamical interactions between different organ systems. This exchange of information is often evaluated with information-theoretic approaches which comprise the use of vector autoregressive (VAR) and state space (SS) models, normally identified with the Ordinary Least Squares (OLS). However, the number of time series to be included in the model is strictly related to the length of data recorded thus limiting the use of the classical approach. In this work, a new method based on penalized regressions, the so-called LASSO, was compared with OLS on physiological time-series extracted from 18 subjects during different stress condi…
Information Dynamics of the Brain, Cardiovascular and Respiratory Network during Different Levels of Mental Stress
In this study, an analysis of brain, cardiovascular and respiratory dynamics was conducted combining information-theoretic measures with the Network Physiology paradigm during different levels of mental stress. Starting from low invasive recordings of electroencephalographic, electrocardiographic, respiratory, and blood volume pulse signals, the dynamical activity of seven physiological systems was probed with one-second time resolution measuring the time series of the &delta